1. Field of the Invention
The present invention is directed to a method for image reconstruction in a computed tomography (CT) apparatus, such as a spiral CT apparatus, as well as to a CT apparatus, such as a spiral CT apparatus, for implementing the method.
2. Description of the Prior Art
A spiral CT (computed tomography) apparatus having a radiation source movable around an examination subject from which a fan-shaped ray beam emanates, and having a detector with a number of lines of detector elements (detector lines) that receives the fan-shaped ray beam, wherein the examination subject and the detector are displaceable relative to one another in the direction of the system axis for the implementation of an examination. It is known to operate such a system to register a number of projections each with several lines of detector elements for a number of projection angles and positions along the system axis, wherein the same lines of detector elements are employed for the registration of all projections. An image is reconstructed from the registered projections.
CT systems of this type are disclosed, for example, in German OS 196 47 435, U.S. Pat. No. 5,682,414 and German OS 42 24 249 as well as U.S. Pat. No. 5,291,402.
For spiral exposures with a CT apparatus that has a detector with a single line of detector elements, an interpolation between the measured values lying in front of and behind the image plane is implemented for generating projections in the desired image plane for each projection angle.
Two interpolation methods are currently most common. In the first, a linear interpolation is undertaken between two measured projections lying closest to the image plane, these having been registered at the same projection angle xcex1 but in different revolutions. This type of interpolation is referred to as 360LI interpolation. In the second method, interpolation is carried out between two sets of measured values lying closest to the image plane, one set of these values having been registered at the projection angle xcex1dxe2x80x2, the other set at the projection angle xcex1cxe2x80x2, complementary thereto. The relation xcex1cxe2x80x2=xcex1dxc2x1Π applies for th e central channel of the detector. This type of interpolation is referred to as 180LI interpolations. It supplies narrower effective slice widths (characterized, for example, by the full width at half-maximum FWHM) than the 360Ll interpolation given the same pitch. As a tradeoff, the image noise is increased compared to 360LI interpolation given the same output power of the X-ray tube (same mA value) and the artifact susceptibility is greater. Both types of interpolation are schematically illustrated in FIG. 1, which shows the projection angle xcex1 as a function of the detector position in the z-direction during a spiral scan for the pitch p=2 normalized onto the collimated width d of a line of detector elements of the detector, i.e. the collimated slice thickness.
In a CT apparatus having multi-line detectors, the reconstruction of spiral data with exact and approximative methods described in German PS 196 14 223 that in fact take the exact geometry into consideration, but this is very calculation-intensive and therefore is not particularly suited for use in a commercial CT apparatus.
For low line numbers M (for example, Mxe2x89xa65), the angle of inclinationxe2x80x94also referred to as the cone anglexe2x80x94of the X-rays (referred to as measuring rays) incident onto the detector relative to a plane perpendicular to the z-axis of the CT apparatus (also referred to as the system axis) can be neglected for reducing the calculating outlay, and the 180LI and 360LI interpolations that are standard for a CT apparatus with a detector having only one line of detector elements can be transferred to multiple detector lines. This is the reconstruction method that is employed in the 2-line CT scanner xe2x80x9cElscint Twinxe2x80x9d (see xe2x80x9cDual-slice versus single-slice spiral scanning: Comparison of the physical performances of two computed tomography scannersxe2x80x9d, Yun Liang and Robert A. Kruger, Med. Phys. 23(2), Febuary 1996, pp. 205-220).
In a presentation analogous to FIG. 1, the principle of the 180LI and 360LI interpolation transferred onto a number of lines is shown in FIG. 2 for the pitch p=3 with reference to the arbitrarily selected example of a CT apparatus having a detector with four lines of detector elements. The pitch p is the feed in z-direction per revolution of the radiation source with reference to the collimated width d of a line of detector elements of the detector, i.e. the collimated slice thickness. The basic problems in the standard multi-line spiral interpolation become clear from FIG. 2:
First, in order to generate data for a predetermined projection angle by interpolation, these data corresponding to a corresponding projection in the desired image plane acquired with a detector having only one line of detector elements, the contribution of a number of projections from different revolutions of the spiral scan must be taken into consideration. The interpolation weightings for a specific projection are thus dependent on the z-position of other projections. Given realization on a computer, this makes the processing of the individual projections more difficult. Dependent on the pitch p, moreover, multiple scans occur (in FIG. 2, for example, at line 1 and line 4 that scan the same z-positions in successive revolutions), which have to be taken into consideration in the calculation of the interpolation s weightings, making the interpolation more computationally complicated.
Second given pitch values pxe2x89xa7M (M is the number of lines of the detector), a 180LI interpolation must be implemented if the slice sensitivity profile is not to spread unacceptably. For illustration, the full wave at half-maximum FWHM of the slice sensitivity profile occurring given 180LI and 360LI interpolation as function of the pitch value p is shown in FIG. 3 for the example of the detector having four lines of detector elements.
180LI interpolation given a detector with one line of detector elements means that interpolation is generally carried out between a direct ray and the ray complementary thereto. The situation is more complicated given a detector having a number of lines. In that case, 180LI interpolation means that interpolation is always carried out between the two measured values that lie closest to the image plane. Dependent on the pitch value p and the position of the image plane in the z-direction, interpolation for a specific projection angle xcex1 is carried out either between direct measured values, namely when these lie closer to the image plane, or between a direct measured value and a measured value complementary thereto when these lie closer to the measured plane.
When, however, interpolation is carried out between direct and complementary measured values given a projection angle xcex1d, the complementary measured value at xcex2c=xe2x88x92xcex2d must be found for every measured value identified by th e direct projection angle xcex1d and the corresponding fan angle xcex2d. The projection angles xcex1d and xcex1cxe2x80x2 of direct and complementary projections are offset by exactly 180xc2x0 only in the rotational center, i.e. for xcex2d=xcex2c=0. The relations
xcex2c=xe2x88x92xcex2d
xcex1c=xcex1d+2xcex2+Πxe2x80x83xe2x80x83(1)
apply in the general case, i.e. the complementary measured value at xcex2c for each direct measured value characterized by the projection angle xcex1d and the fan angle xcex2d, is from a different projection, that accordingly was registered at a different z-position. Interpolation weightings that are independent of fan angle therefore must be used in the 180LI interpolation, and the contributions of different complementary projections for each direct projection must be considered, this immensely increasing the calculating outlay.
Third, the standard deviation of the pixel noise measured in the image arises from the quadratic sum of all interpolation weightings for each pitch value p. These interpolation weightings are pitch-dependent in the 180LI and in the 360LI interpolations. Given a fixed output power of the X-ray tube, the pixel noise to be set for each pitch value p is thus also defined. This pixel noise exhibits unexpected and unwanted dependencies on the pitch p. For a detector having four lines of detector elements, for example, the measured values of all four detector lines fall onto the same z-positions in successive revolutions given the pitch p=1. They can therefore be simply averaged before the interpolation. As a result, a dose accumulation by the a factor of four, and therefore a halving of the pixel noise, occur compared to a detector having only one line of detector elements. When the pitch is increased only slightly, for example to p=1.1, this multiple scan is eliminated. A narrower slice sensitivity profile is then obtained in the 180LI and the 360LI interpolations, but at the cost of the same pixel noise as in a one line detector.
With conventional 180LI and 360LI interpolations, it is not possible given low pitch values (for example, p=1.1, as above), to utilize the overlapping scanning in the z-direction (i.e., the lines of the detector successively acquire the same z-region in different revolutions) for the purpose of reducing the pixel noise. In particular, it is also not possible to employ only a freely selectable part of the data available overall at the z-position Zima (the index xe2x80x9cimaxe2x80x9d stands for image) for the reconstruction. It is thus also not possible to set a freely selectable compromise between reduced pixel noise(on the basis of the overlapping scanning) and improved time resolution of the reconstruction.
An object of the present invention is to provide a method of the type initially described that is improved in terms of the slice sensitivity profile as well as a spiral CT apparatus for the implementation of such a method.
The above object is achieved in accordance with the principles of the present invention in a method for image reconstruction for a CT apparatus, and in a CT apparatus for implementing the method, wherein acquisition of the data needed for an image reconstruction of an image plane at a specific position in the system axis ensues by combining measured values for each individual projection angle needed for the image reconstruction, that are registered exclusively for this projection angle with different lines of detector elements, to form data apparently registered with a detector having only one line of detector elements, by conducting a weighting of the measured values for the projections which enter into the image reconstruction. The image reconstruction is then conducted using an algorithm for operating on data from a detector having only one line of detector elements.
The invention thus combines weightings undertaken independently of one another for the individual projections with an algorithm conventionally employed for a detector having only one line of detector elements for the image reconstruction. The inventive method has the following advantages:
First, the weighting referred to below as spiral weighting is undertaken separately for each projection angle for the projections registered with the individual lines of detector elements of the detector, called multi-line projection below. Differing from the conventional 180LI or 360LI interpolation, the z-position of projections that were acquired at other projection angles, plays no part in the calculation of the weightings for the individual projections of a multi-line projection (spiral weightings) at the projection angle xcex1. The processing of the individual projections can thus quite simply ensue sequentially.
Secondly, the spiral weighting is undertaken in fan data. For each line i of the detector, the interpolation weighting for each projection xcex1 is dependent on its z-position and on the z-position of the desired image. By contrast or 180Li interpolation, however, it is independent of the fan angle xcex2. Differing from 360LI interpolation, however, the slice sensitivity profile of the inventive method remains acceptably narrow up to the pitch value p=2M. The artefact susceptibility of the inventive method is comparable to that of 180LI interpolation.
Third, given small values of the pitch p with overlapping scanning in the z-direction, the region of the projection angle contributing to the image can be arbitrarily selected within certain limits. Without limitation in the image quality, any desired compromise between improved dose utilization and reduced pixel noise (due to the overlapping scanning) and improved time resolution of the reconstruction thus can be set.
The reason why these advantages can be achieved shall be explained below:
When it is established as a condition, that a full wave at half-maximum FWHM of the slice sensitivity profile is to be achieved that corresponds to that of a 360LI interpolation given the pitch 1, i.e. that remains smaller than approximately 1.3 times the collimated width of a detector line (FWHMxe2x89xa61.3 d), then a 180LI interpolation must be employed in known methods given pitch values Mxe2x89xa6pxe2x89xa62M.
In order to achieve FWHMxe2x89xa61.3d for Mxe2x89xa6pxe2x89xa62M, it is actually not necessary to unconditionally interpolate between the measured values that are the closest neighbors to the image plane, as occurs, however, in the 180LI interpolation. Instead, it would be adequate to interpolate exclusively between direct measured values in front of and behind the image plane as long as these are at no greater distance from one another than the width of a detector line, even when a complementary measured value lies closer to the image plane. With increasing pitch, however, the spacing of the available, direct measured values in the edge regions of the projection angle interval employed for the reconstruction becomes clearly greater than the width of a detector line because interpolation is no longer carried out between the measured values of the individual detector lines measured for the same projection angle. Instead, direct measured values offset by 360xc2x0 from various revolutions must be employed. This explains the increase in the effective layer thickness and the considerable degradation of the slice profile given the 360LI interpolation wherein, of course, interpolation is only carried out between direct measured values (see FIG. 3). According to conventional methods, a complicated interpolation between direct and complementary measured values would have to be undertaken in these projection angle regions. In these critical projection angle regions, wherein an interpolation would be required between direct and complementary rays, the inventive method replaces this with the use of the direct rays by themselves. Inconsistencies at the boundaries of the reconstruction interval due to lacking interpolation can be effectively suppressed in the technique by a known transition weighting with an adequately smooth function that is undertaken in the subsequent overscan or sub-revolution reconstruction. In view of the artefact behavior, thus, this transition weighting replaces the lacking spiral interpolation.
In an embodiment of the invention, the image reconstruction can be undertaken both on the basis of a known sub-revolution reconstruction as well as on the basis of a known overscan reconstruction. In the case of a sub-revolution reconstruction, data are utilized that were acquired during a revolution angle of the radiation source of at most 2Π. In the case of an overscan reconstruction, a dataset is utilized that was acquired during a revolution angle of the radiation source of more than 2Π.
Independently of the type of image reconstruction, it is possible in the inventive method to undertake the combination of the data with respect to the projection angles to be taken into consideration such that a combination of direct and complementary measured values is not carried out, avoiding the disadvantages connected with this measure.
In a preferred embodiment of the invention, a combination of the data for the projection angles to be taken into consideration ensues sequentially, so that the outlay for an electronic computer for implementation of the inventive method is low.
An inventive spiral CT apparatus contains a parallel computer. The preferably sequential combination of the data can then ensue especially fast.
An inventive apparatus is a spiral CT apparatus wherein the region of the projection angles to be taken into consideration in the image reconstruction is freely selectable. Without limiting the image quality, it is then possible to realize any desired compromise between improved utilization of the x-ray dose and reduced pixel noise, and improved time resolution.
In an inventive spiral CT apparatus, the relative motion between examination subject and the radiation source and detector ensues with variable direction and/or variable speed. This is possible since only data that are derived from the same revolution of the radiation source are combined with respect to each projection angle.